The objective of transfer learning is to enhance estimation and inference in a target data by leveraging knowledge gained from additional sources. Recent studies have explored transfer learning for independent observations in complex, high-dimensional models assuming sparsity, yet research on time series models remains limited. Our focus is on transfer learning for sequences of observations with temporal dependencies and a more intricate model parameter structure. Specifically, we investigate the vector autoregressive model (VAR), a widely recognized model for time series data, where the transition matrix can be deconstructed into a combination of a sparse matrix and a low-rank one. We propose a new transfer learning algorithm tailored for estimating high-dimensional VAR models characterized by low-rank and sparse structures. Additionally, we present a novel approach for selecting informative observations from auxiliary datasets. Theoretical guarantees are established, encompassing model parameter consistency, informative set selection, and the asymptotic distribution of estimators under mild conditions. The latter facilitates the construction of entry-wise confidence intervals for model parameters. Finally, we demonstrate the empirical efficacy of our methodologies through both simulated and real-world datasets.

Deep neural networks are powerful tools to model observations over time with non-linear patterns. Despite the widespread useof neural networks in such settings, most theoretical developments of deep neural networks are under the assumption of independent observations, and theoretical results for temporally dependent observations are scarce. To bridge this gap, we study theoretical properties of deep neural networks on modeling non-linear time series data. Specifically, non-asymptotic bounds for prediction error of (sparse) feed-forward neural network with ReLU activation function is established under mixing-type assumptions. These assumptions are mild such that they include a wide range of time series models including auto-regressive models. Compared to independent observations, established convergence rates have additional logarithmic factors to compensate for additional complexity due to dependence among data points. The theoretical results are supported via various numerical simulation settings as well as an application to a macroeconomic data set.

There is increasing interest in identifying changes in the underlying states of brain networks. The availability of large scale neuroimaging data creates a strong need to develop fast, scalable methods for detecting and localizing in time such changes and also identify their drivers, thus enabling neuroscientists to hypothesize about potential mechanisms. This paper presents a fast method for detecting break points in exceedingly long time series neurogimaging data, based on vector autoregressive (Granger causal) models. It uses a multi-step strategy based on a regularized objective function that leads to fast identification of candidate break points, followed by clustering steps to select the final set of break points and subsequent estimation with false positives control of the underlying Granger causal networks. The latter provide insights into key changes in network connectivity that led to the presence of break points. The proposed methodology is illustrated on synthetic data varying in their length, dimensionality, number of break points, strength of signal and also applied to EEG data related to visual tasks.

Traffic signals as part of intelligent transportation systems can play a significant role in making cities smart. Conventionally, most traffic lights are designed with fixed-time control, which induces a lot of slack time (unused green time). Actuated traffic lights control traffic flow in real time and are more responsive to the variation of traffic demands. For an isolated signal, a family of time series models, such as autoregressive integrated moving average (ARIMA) models, can be beneficial for predicting the next cycle length. However, when there are multiple signals placed along a corridor with different spacing and configurations, the cycle length variation of such signals is not just related to each signal’s values, but it is also affected by the platoon of vehicles coming from neighboring intersections. In this paper, a multivariate time series model is developed to analyze the behavior of signal cycle lengths of multiple intersections placed along a corridor in a fully actuated setup. Five signalized intersections have been modeled along a corridor, with different spacing among them, together with multiple levels of traffic demand. To tackle the high-dimensional nature of the problem, a penalized least-squares method is utilized in the estimation procedure to output sparse models. Two proposed sparse time series methods captured the signal data reasonably well and outperformed the conventional vector autoregressive model—in some cases up to 17%—as well as being more powerful than univariate models, such as ARIMA.